Statement And Truth Flashcards
What is a statement?
A sentence with a true of false value
What are axioms?
Statements which we do not attempt to prove but assume to be true
What are theorems?
Statements deduced from axioms by mathematical proof
What is an implication, and when is it false?
It is a conditional statement of the form “if p, then q”. P is called the antecedent and q is the consequent.
An implication is false only when p is true and q is false. It’s there in all other situations.
What is the converse of P => Q?
Q => P
What is the contrapositive of P => Q
~Q => ~P
What is a double implication?
1) P <==> Q
2) P if and only if Q
3) (P => Q) ^ (Q => P)
What is a Lemma?
A proposition used in demonstration of another proposition
What is a Corollary?
Propostion that is direct consequent of another proposition
What is a statement?
A sentence in which we can decide it it’s truth value and is not vague.
What is a quantifier?
An expression that says how many elements there are to be considered.
What is a predicate?
state, affirm, or assert (something) about the subject of a sentence or an argument of a proposition.
When is an argument valid?
Whenever the conjunctions of the premises is true
When is an argument sound?
If it is valid and the premises are true.
